The eutectoid composition for an iron-carbon alloy is approximately 0.76% carbon. When cooled from the alpha phase to room temperature at this composition, the alloy undergoes a transformation where it changes from austenite (gamma phase) to a mixture of ferrite and cementite, known as pearlite. This transformation occurs at around 727°C, leading to the formation of a layered microstructure that enhances the mechanical properties of the alloy. The cooling rate can significantly influence the resulting microstructure and, consequently, the material's hardness and ductility. The referenced notes provide detailed insights into phase diagrams and microstructural changes during this cooling process, illustrating the importance of controlling the cooling rate to achieve desired material characteristics.